4 MW, 50 Hz, 10 GeV, 1 ns (rms), FFAG Proton Driver Study

G H Rees, RAL

4 MW Proton Driver Arrangement

Muon yields optimal for 6 - 10 GeV (S Brooks)

Choose 10 GeV, 50 Hz to ease target shocks

Choose 3 GeV booster for a 3 – 10 GeV FFAG

Choose between 1, 50 Hz or 2, 25 Hz boosters

Choose 0.18 GeV H‾ linac for low bunch areas

Choose 5 bunches at h = 5 for RCS booster(s)

Transfer all 5 (1013 protons/bunch) to the FFAG

Compress adiabatically (h = 30 & 180, R = 2Rb)

Longitudinal bunch area

A, the longitudinal bunch area (in eV sec), =

(8Rα/(ch))((2 V(I-sc)Eo)/(h))½

For a small longitudinal bunch area, choose

a low value of injection energy and ring radius

Choose Eo ( - 1) = 0.18 GeV and R 50.0 m

Choose the bunch & harmonic number (h) = 5

Compressed bunch area needed 0.66 eV sec

4 MW, Proton Driver Layout

0.18 GeV H ‾ Achromat

0.18 GeV H ‾ Linac

10 GeV, 50 Hz, N = 5, FFAGwith 1013 protons per bunch

3 GeV, 50 Hz, h = 5, RCS(1 at 50 Hz, or 2 at 25 Hz)

FFAG Design Criteria

For compression of the 5 bunches at 10 GeV: Design for a gamma-t value at 10 GeV 18.5Design for longitudinal bunch areas 0.66 eV sAdiabatic acceleration & comp. with h = 30, 180

Design the FFAG ring with lattice insertions, toease injection, ejection & beam loss collectionUse two insertions to allow most flexibility, eg:21 normal and 13 insertion cells per insertion

Lattice Cell OptionsNormal cell Insertion cell Magnet types

Doublet D D1 + T0 + D2 2 + 7Triplet T T1 + T2 + T1 2 + 4Pumplet P1 P2 3 + 3

Easiest solution is to match the two, pumplet cells: P1 has a smaller β-range than either D or T The insertion has only one type of cell, P2 P2 has the smallest closed orbit “lever arm”

Dispersion suppressors (2) are not included in the insertions as too many of them are needed

10 GeV, Normal & Insertion Cell Layouts

bd(-) BF(±) BD (+) BF(±) bd(-)

O 0.5 0.5 0.5 0.5 O

0.45 1.0 1.6 1.0 0.45

0.77 Normal cell (5.294º, 8.037 m) 0.77 2.25 Insertion cell (5.294º, 11.0 m) 2.25 There are two superperiods of 21 normal &13 insertion cells

Betatron tunes at 10 GeV are 19.2 (Qh) and 13.7 (Qv) Ring circumference = 2 (99.24125) m

FFAG Lattice Design

Use the five-unit cell of the isochronous, muon ring

Arrange ~ matching for a normal and insertion cell

Arrange integer, insertion tunes eg Qh = 4 & Qv = 3

The normal cells in an insertion are then matched

Seek unchanged closed orbits on adding insertions

by varying the normal cell field gradients and tunes

Then, dispersion match is almost exact for insertions

Small ripple remains in βh and βv (max) in insertions

Study Progress

Orbits evaluated at: 10.0, 9.6, 9.2 and 8.8 GeVSatisfactory matching found at these energies

P- driver bends; bd : BF : BD ~ - 0.23 : 1.0 : 0.23(Muon ring bends; bd : BF : BD ~ - 1.0 : 1.0 : 1.0)

Dispersion match requires lower Qh in normal cells:Qh = 19.2, 19.16,…19.08 at 10.0, 9.6,…8.8 GeVNext, switch integer tunes from the insertion to thenormal cells so tunes may be raised again to 19.2

10 GeV FFAG versus RCS

Required is one FFAG ring, but two RCS(s)Operation is allowed at 50 Hz instead of 25 Hzwith 5 1013 ppp at target, instead of 1014 ppp Shock per pulse on the target is thus halved

FFAG allows acceleration over more of cycle FFAG is more flexible for holding of bunches FFAG has a more rugged vacuum chamberFFAG does not need ac magnet power supply